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Bounded‐influence rank estimation in the linear model
Author(s) -
Wiens Douglas,
Zhou Julie
Publication year - 1994
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315586
Subject(s) - bounded function , rank (graph theory) , estimator , residual , mathematics , monte carlo method , function (biology) , variety (cybernetics) , mathematical optimization , statistics , algorithm , combinatorics , mathematical analysis , biology , evolutionary biology
We introduce and study a class of rank‐based estimators for the linear model. The estimate may be roughly described as being calculated in the same manner as a generalized M‐estimate, but with the residual being replaced by a function of its signed rank. The influence function can thus be bounded, both as a function of the residual and as a function of the carriers. Subject to such a bound, the efficiency at a particular model distribution can be optimized by appropriate choices of rank scores and carrier weights. Such choices are given, with respect to a variety of optimality criteria. We compare our estimates with several others, in a Monte Carlo study and on a real data set from the literature.